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Solving Helmholtz problems with the boundary element method using direct radial basis function interpolation

机译：使用直接径向基函数插值法用边界元方法求解亥姆霍兹问题

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摘要

In the present study, a direct interpolation technique that uses radial basis functions is applied to the boundary element method integral term, which refers to inertia, in the Helmholtz equation; consequently, free vibration frequencies and corresponding amplitudes can be determined from an eigenvalue problem solution. The proposed method, which has already been successfully applied to scalar problems governed by the Poisson equation, does not require standard domain integration procedures, which employ cell discretisation, and is more robust than the dual-reciprocity technique. Although similar to the latter in some aspects, because it uses radial basis functions and their primitives for interpolation, the proposed methodology is more general. It allows the immediate use of interpolation functions of any type, and there are no convergence or monotonicity problems as the number of basis points is increased.
机译：在本研究中，将使用径向基函数的直接插值技术应用于边界元素法积分项，该项在Helmholtz方程中是指惯性。因此，自由振动频率和相应的振幅可以从特征值问题解决方案中确定。所提出的方法已经成功地应用于由Poisson方程控制的标量问题，不需要标准的域积分程序，该程序采用了单元离散化，并且比双对等技术更健壮。尽管在某些方面与后者相似，但由于它使用径向基函数及其基元进行插值，因此所提出的方法更为通用。它允许立即使用任何类型的插值函数，并且随着基点数量的增加，不存在收敛或单调性问题。

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  • 来源
    《Engineering analysis with boundary elements》 |2015年第12期|218-225|共8页
  • 作者

    Carlos Friedrich Loeffler; Webe Joao Mansur; Hercules de Melo Barcelos; Andre Bulcao;

  • 作者单位

    Programa de Pos-Graduacao em Engenharia Mecanica, UFES - Centro Tecnologico, Avenida Fernando Ferrari, 540, Bairro Goiabeiras, 29075-910 Vitoria, ES, Brazil;

    Programa de Pos-Graduacao em Engenharia Civil, COPPE/UFRJ - Centro de Tecnologia, Bloco B, Ilha do Fundao, 21941-972 Rio de Janeiro, RJ, Brazil;

    Programa de Pos-Graduacao em Engenharia Mecanica, UFES - Centro Tecnologico, Avenida Fernando Ferrari, 540, Bairro Goiabeiras, 29075-910 Vitoria, ES, Brazil;

    PETROBRAS, Centro de Pesquisa e Desenvolvimento Leopoldo A. Miguez de Mello, Avenida Horacio de Macedo 950, Ilha do Fundao, 21941-915 Rio de Janeiro, RJ, Brazil;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Helmholtz problems; Eigenvalues; Boundary element method;

    机译：亥姆霍兹问题;特征值;边界元法;

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